Complete the Magic Square

You are given a partially filled \( n \times n \) grid. Your task is to complete this grid to form a magic square, where the sum of the numbers in each row, each column, and both main diagonals are equal. For a magic square of size \( n \), this common sum (the magic constant) is given by \( M = \frac{n(n^2+1)}{2} \).

The grid may have some pre-filled numbers, and zero represents an empty cell. You must fill in the empty cells with numbers from \( 1 \) to \( n^2 \) (each exactly once) such that the final grid forms a magic square. If it is possible to complete the grid, output POSSIBLE followed by the completed grid. Otherwise, output IMPOSSIBLE.

It is guaranteed that \( n = 3 \) for all test cases.

inputFormat

The first line contains a single integer \( n \) (which is 3 in all test cases). Each of the next \( n \) lines contains \( n \) integers representing the grid. Empty cells are denoted by 0.

Example:

3
0 0 0
0 0 0
0 0 0

outputFormat

If it is possible to complete the grid to form a magic square, print POSSIBLE on the first line, and then print the \( n \) lines of the completed magic square (each line contains \( n \) space-separated integers). Otherwise, print IMPOSSIBLE.

## sample

3
0 0 0
0 0 0
0 0 0

POSSIBLE
2 7 6
9 5 1
4 3 8

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